Positions on intrinsic properties and causal/nomic roles
Warning: another pointless exercise in conceptual geography.
Can intrinsic properties have their causal/nomic role essentially? It seems not. Suppose something x is P. If P essentially occupies a certain causal role, say being such that all its instances attract one another, we can infer from x's being P that either there are no other P-things in x's surrounding or x and the other things will (ceteris paribus) move towards one another. But if we can infer from x's being P what happens in x's surrounding, P cannot be intrinsic. Being intrinsic means belonging to things independently of what goes on in their neighbourhood.
In other words, I suggest that the principle of recombination, according to which arbitrary arrangements of intrinsic duplicates of things are possible, is analytic: that's just what "intrinsic duplicate" means.
Consider Shoemaker/Swoyerism, the view that spin, charge etc. play their causal/nomic role essentially. On my understanding, this view does not reject the recombination principle, but rather the assumption that spin, charge etc. are intrinsic. (What if a Shoemaker/Swoyerist claims that some clearly intrinsic property -- say, being mereologically complex -- essentially occupies a certain causal/nomic role? I guess I'll find such a claim unintelligible.)
Maybe some causal/nomic roles can essentially belong to intrinsic properties. If Q is intrinsic, it could be essential for P that any P is Q. This would not make P extrinsic. But that's a strange kind of 'causal/nomic role'. Ordinarily, a property's causal/nomic role determines how things with that property interact with other things, not only with themselves (or their parts). Let me reserve "causal/nomic role" for such ordinary roles.
So we have:
No-Intrinsic-Role-Properties) If P is intrinsic and occupies a certain causal/nomic role, it could have failed to occupy that role.
One might suspect that No-Intrinsic-Role-Properties entails
Quidditism) There are distinct possibilities that differ only in which intrinsic properties occupy which causal/nomic roles.
More precisely, what Quidditism claims is that there are intrinsic properties P, Q and worlds w, w' completely described by descriptions D_w, D_w' such that D_w and D_w' differ only by replacing all occurrences of "P" with "Q" and vice versa (and there is at least one such occurrence in D_w or D_w').
So does No-Intrinsic-Role-Properties entail Quidditism? No. For one, Quidditism presupposes that intrinsic properties can occupy causal/nomic roles. Proponents of Shoemaker/Swoyerism might deny that. Secondly, if P is intrinsic and plays a certain role R, No-Intrinsic-Role-Properties only says that there is a world where P does not play R. It does not say that in that world, P has traded places with some other intrinsic property Q. There might be no such world.
For example, suppose in w, P only belongs to objects with exactly 11 parts. Then no intrinsic property that essentially belongs to mereological atoms could take over P's role. And maybe there is no other causally active property Q that can belong to objects with 11 parts only. (This is especially plausible if one rejects alien properties and has certain views about what it takes to be causally active.)
At any rate, the intrinsic properties having exactly 11 parts and having no proper parts refute
Extreme Quidditism) For any two intrinsic properties, there are distinct possibilities that differ only in which of them occupies which causal/nomic role.
(Notice that Lewis endorses Extreme Quidditism only for fundamental properties, not for intrinsic properties in general, and even there he restricts it to properties of the same 'category'. So what I call "Quidditism" is in some ways stronger and in others weaker than Lewis's "Quidditism".)
Lewis argues that Quidditism entails
Noumenalism) Some things have an intrinsic nature of which we are (in principle) ignorant.
What this means depends on how exactly knowledge and ignorance of nature is understood: Certainly Quidditism does not preclude de re knowledge of intrinsic properties. Taking doxastic possibilities as primitive, let's say that one knows the intrinsic nature of an object if the object has the very same intrinsic properties in all one's doxastic possibilities. More or less equivalently, one knows the intrinsic nature of an object if one recognizes as true a (possibly private) sentence whose A-intension rules out that the object has any other intrinsic nature.
Quidditism entails Noumenalism (in this sense) if we can know of a thing's intrinsic properties only via its causal/nomic relation to other things. Then we could not distinguish between two things that differ only in which intrinsic properties play which causal roles. I don't know if that assumption is true.
Does Noumenalism conversely entail Quidditism? Not quite. If Noumenalism is true, there is an intrinsic property P belonging to objects of which we cannot know that they have P. If Quidditism is false, no causally active intrinsic property could trade places with any other such property. Both conditions are satisfied if P is not causally active, and also if it is impossible for us to know P's causal/nomic role. (If we knew that x has a property with such-and-such causal/nomic role in the sense that in all our doxastic possibilities x has a property with that role, and if no other property could possibly occupy that role (Quidditism is false), then we would also know in the relevant sense that x has P.)
Lewis's assumption that we can know a thing's intrinsic properties only via its causal/nomic relations resembles (but only resembles) the assumption of Pettit and others that we can only recognize response-dependent or dispositional properties of objects. Again, from a Shoemaker/Swoyer perspective, one could argue that the world is 'dispositional all the way down', so that it wouldn't follow that we remain ignorant of anything. Even if one rejects this view by endorsing something like
No-bare-dispositions) An object's dispositions are always determined by its non-dispositional properties,
something like noumenalism doesn't necessarily follow unless
Independent-Grounds) There are distinct possibilities that differ only in which non-dispositions properties underlie which dispositions,
which resembles (but only resembles) Quidditism.
"Quidditism entails Noumenalism (in this sense) if we can know of a thing's intrinsic properties only via its causal/nomic relation to other things. Then we could not distinguish between two things that differ only in which intrinsic properties play which causal roles. I don't know if that assumption is true."
I find it intruiging that you're unsure about this. How else would be come we to know the intrinsic properties except via their causal links (except in the obviously a priori case where the intrinsic property in question is some "logical" property)? To be fair, doesnt Lewis think that if humility is true, its contingently true? Is that where you're coming from?